Finite Group Databasebeta

← Prev (#26003195) Next (#26003197) →

C4×H(5,𝔽2)×D43 #26003196

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

Aliases

direct productC4×H(5,𝔽2)×D43

Splittings

FittingC4×H(5,𝔽2)×C43 ⋊ C2
SylowC43 ⋊ C2×C4×H(5,𝔽2)

Subgroups

subgroupG/H
centerC2×C4C24×D43
commutatorC2×C43C25×C4
FrattiniC22C25×D43
FittingC4×H(5,𝔽2)×C43C2
socle, cosocleC22×C43C26
prime radicalC2×H(5,𝔽2)×D43C2
hypercenterC4×H(5,𝔽2)D43
hypocenterC43C2×C4×H(5,𝔽2)
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×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, 1076167);