Finite Group Databasebeta

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C4×#14583081 #25102502

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#14583081

Splittings

FittingC4×C4⋊Q8×C43 ⋊ C2
SylowC43 ⋊ C4×#456

Subgroups

subgroupG/H
centerC2×C4#13063293
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×C4⋊Q8×C43C2
socleC22×C43C2×#120
prime radicalC2×#13063373C22
cosocleC22×C4×C43C24
hypercenterC4×C4⋊Q8D43
hypocenterC43C4×#456
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×C4⋊Q8

1358 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 175473);