Finite Group Databasebeta

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#100×Dic86 #25113158

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

Aliases

direct product#100×Dic86

Splittings

SylowC43 ⋊ Q8×#100

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#100×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×D4×C43C23
cosocleC22×C4×C43C24
hypercenterC4×#100D43
hypocenterC43Q8×#100
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#100

1198 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

979 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 186129);