#1342×D₇₉ #34198425

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

Aliases

direct product

#1342×D₇₉

Splittings

Fitting	C₇₉×#1342 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1342

Subgroups

	subgroup	G/H
center	C₂	#327×D₇₉
commutator	C₂×C₈×C₇₉	C₂²×C₄
Frattini	C₂×M₁₆	C₂²×D₇₉
Fitting	C₇₉×#1342	C₂
socle	C₂×C₇₉	C₂×#327
prime radical	C₂³×D₇₉	SD₁₆
cosocle	C₂×M₁₆×C₇₉	C₂³
hypercenter	#1342	D₇₉
hypocenter	C₇₉	C₂×#1342
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #1342

428 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 81 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 111
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 3 generators on 111 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,82,86,95)(81,87,90,104)(83,97,100,109)(84,94,85,93)(88,105,107,111)(89,102,101,103)(91,106,108,96)(92,99,110,98);(80,81,84,89,86,90,85,101)(82,91,93,105,95,108,94,111)(83,96,98,88,100,106,99,107)(87,97,102,110,104,109,103,92)

Conjugacy classes & character table

820 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 79724);