#1369×D₇₉ #34199829

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈ · Schur multiplier (H₂) = C₂²

Aliases

direct product

#1369×D₇₉

Splittings

Fitting	C₇₉×#1369 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1369

Subgroups

	subgroup	G/H
center	C₄	#106×D₇₉
commutator	C₈×C₇₉	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₇₉
Fitting	C₇₉×#1369	C₂
socle	C₂×C₇₉	C₂×#334
prime radical	C₂²×D₇₉	#108
cosocle	C₄×C₈×C₇₉	C₂³
hypercenter	#1369	D₇₉
hypocenter	C₇₉	C₂×#1369
LCS	G ▷ C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1369

222 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 101 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)(80,82,83,94,85,96,100,95,87,98,101,109,86,97,84,102)(81,88,89,93,91,104,99,108,92,105,90,106,103,111,107,110);(80,81,84,90,86,91,101,107,87,92,100,89,85,103,83,99)(82,93,95,104,97,108,94,105,98,106,102,111,96,110,109,88)

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 81128);