Finite Group Databasebeta

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C4×#14583122 #25102834

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14583122

Splittings

FittingC4×C4⋊C8×C43 ⋊ C2
SylowC43 ⋊ C4×#464

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C4⋊C8×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×C4⋊C8D43
hypocenterC43C4×#464
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×C4⋊C8

1016 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 175805);