Finite Group Databasebeta

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C2×H(5,𝔽2)×Dic43 #26003201

order11008
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC2×H(5,𝔽2)×Dic43

Splittings

SylowC43 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC23C24×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
Fitting, prime radicalC22×H(5,𝔽2)×C43C2
socleC23×C43C25
cosocleC22×C43C26
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×C4×H(5,𝔽2)
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×H(5,𝔽2)

12378 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076172);