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C2×#19134423 #25094357

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#19134423

Splittings

FittingC2×C4×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C2×#1762

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×C4⋊C4×C43C2
socleC24×C43C2×D4
prime radicalC23×D172C22
cosocleC22×C4×C43C24
hypercenterC2×C4×C4⋊C4D43
hypocenterC43C2×#1762
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×C4×C4⋊C4

2118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167328);