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C8×#13063245 #24987363

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4

Aliases

direct productC8×#13063245

Splittings

FittingC8×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C8×#102

Subgroups

subgroupG/H
centerC22×C8C22⋊D43
commutatorC4×C43C2×C4×C8
FrattiniC2×C42C22×D43
FittingC8×C4⋊C4×C43C2
socleC23×C43C4×D4
prime radicalC22×D172C2×C4
cosocleC2×C42×C43C23
hypercenterC8×C4⋊C4D43
hypocenterC43C8×#102
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C4×C8 ◁ C8×C4⋊C4

606 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 60334);