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C₂²×#1142 #90485

order	448
isoclinism	isoclinic class of #1141
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵

Aliases

Splittings

C₇ ⋊ C₂²×SD₁₆

Subgroups

	subgroup	G/H
center	C₂³	C₂²⋊D₇
commutator, cosocle	C₄×C₇	C₂⁴
Frattini	C₄	C₂³×D₇
Fitting, prime radical	C₂²×C₇×D₄	C₂
socle	C₂³×C₇	D₄
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂²×SD₁₆
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 224

A minimal faithful permutation representation — 4 generators on 19 points:

(5,6,8,10,11,9,7)(13,16)(14,19)(17,18);(6,7)(8,9)(10,11)(12,13,15,18)(14,16,19,17);(3,4);(1,2)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11727400, #11727403, #11727405, …
maximal normal subgroup of	#11727400, #11727403, #11727405, …
maximal quotient of	C₂²×#6382, C₂²×#6384, C₂×#89743, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1247);