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C₂²×#1141 #90483

order	448
isoclinism	isoclinic class of #1141
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

Splittings

Fitting	C₂²×C₇×D₄ ⋊ C₂
Sylow	C₇ ⋊ C₂²×D₈

Subgroups

	subgroup	G/H
center	C₂³	C₂²⋊D₇
commutator, cosocle	C₄×C₇	C₂⁴
Frattini	C₄	C₂³×D₇
Fitting	C₂²×C₇×D₄	C₂
socle	C₂³×C₇	D₄
hypercenter	C₂²×D₄	D₇
hypocenter	C₇	C₂²×D₈
LCS	G ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×D₄

338 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)(14,16)(15,18)(17,19);(3,4);(1,2)

Conjugacy classes & character table

88 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#11727401, #11727402, #11727404, …
maximal normal subgroup of	#11727401, #11727402, #11727404, …
maximal quotient of	C₂²×#6381, C₂²×#6383, C₂×#89739, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 1245);