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Q₃₂×D₉₇ #20261161

order	6208
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

Q₃₂×D₉₇

Splittings

Fitting	Q₃₂×C₉₇ ⋊ C₂
Sylow	C₉₇ ⋊ C₂×Q₃₂

Subgroups

	subgroup	G/H
center	C₂	D₈×D₉₇
commutator	C₈×C₉₇	C₂³
Frattini	C₈	C₂²×D₉₇
Fitting	Q₃₂×C₉₇	C₂
socle	C₂×C₉₇	C₂×D₈
hypercenter	Q₃₂	D₉₇
hypocenter	C₉₇	C₂×Q₃₂
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈ ◁ Q₃₂

82 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

550 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SD₆₄×D₉₇, Q₆₄×D₉₇, #27144052, …
maximal normal subgroup of	SD₆₄×D₉₇, Q₆₄×D₉₇, #27144052, …
maximal quotient of	#358×D₉₇, #366×D₉₇, #27143592, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6208, 975);