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C₄×Dic₂₈ #89470

order	448
isoclinism	isoclinic class of #1132
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂²

Aliases

C₄×Dic₂₈

Splittings

C₇ ⋊ C₄×Q₁₆

Subgroups

	subgroup	G/H
center	C₂×C₄	D₂₈
commutator	C₄×C₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₇
Fitting	C₄×C₇×C₈	C₂
socle, prime radical	C₂²×C₇	C₂×D₄
cosocle	C₂×C₄×C₇	C₂³
hypercenter	C₄×C₈	D₇
hypocenter	C₇	C₄×Q₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

110 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 3 generators on 27 points:

(1,2,4,6,7,5,3)(12,14,21,25,16,23,15,22)(13,17,24,27,19,26,18,20);(2,3)(4,5)(6,7)(12,13,16,19)(14,20,23,27)(15,24,21,18)(17,25,26,22);(8,9,10,11)

Conjugacy classes & character table

124 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11725272, #11725278, #11725311, …
maximal normal subgroup of	#11725272, #11725278, #11725311, …
maximal quotient of	C₈×Dic₂₈, #11725810, #11725840, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 232);