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C2×C8×#10597010 #23750579

order9536
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#10597010

Splittings

FittingC2×C8×C149 ⋊ C4
derived, SylowC149 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#10597010
commutator, hypocenterC149C2×C4×C8
FrattiniC4C22×#10597010
FittingC2×C8×C149C4
socleC22×C149C42
prime radicalC22×D149C2×C4
cosocleC4×D149C23
LCSG ▷ C149
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#10597010)⋊C16, #34059734, C4×C8×#10597010, …
maximal normal subgroup of(C2×#10597010)⋊C16, #34059734, C4×C8×#10597010, …
maximal quotient ofC2×C8×#11924753, C8×D149⋊C8, C2×#11924753⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1503);