#1403×D₇₉ #34208498

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

Aliases

direct product

#1403×D₇₉

Splittings

Fitting	C₇₉×#1403 ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#1403

Subgroups

	subgroup	G/H
center	C₂	AΣL(1,𝔽₁₆)×D₇₉
commutator	C₂×D₄×C₇₉	C₂²×C₄
Frattini	#124	C₂²×D₇₉
Fitting	C₇₉×#1403	C₂
socle	C₂×C₇₉	C₂×AΣL(1,𝔽₁₆)
prime radical	H(5,𝔽₂)×D₇₉	C₄
cosocle	#124×C₇₉	C₂³
hypercenter	#1403	D₇₉
hypocenter	C₇₉	C₂×#1403
LCS	G ▷ C₂×D₄×C₇₉ ▷ C₂×C₄×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ #124 ◁ #1403

514 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 61 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) = 95
transitive degree	μ_t(G) = 1264

A minimal faithful permutation representation — 3 generators on 95 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 89797);