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H(5,𝔽2)×#88322 #28249751

order13568
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productH(5,𝔽2)×#88322

Splittings

SylowC53 ⋊ C8×H(5,𝔽2)

Subgroups

subgroupG/H
center, FrattiniC2×C4C24×D53
commutatorC2×C53C24×C8
FittingC4×H(5,𝔽2)×C53C2
socleC22×C53C24×C4
prime radicalC2×H(5,𝔽2)×C53C4
cosocleC2×C4×C53C25
hypercenterC4×H(5,𝔽2)D53
hypocenterC53C8×H(5,𝔽2)
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

2422 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1035227);