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C22×C4×#10597010 #23750685

order9536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#10597010
unambiguous semidirect productD149⋊(C2×C42)

Splittings

FittingC22×C4×C149 ⋊ C4
derived, SylowC149 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#10597010
commutator, hypocenterC149C22×C42
FrattiniC2C23×#10597010
FittingC22×C4×C149C4
socleC23×C149C2×C4
prime radicalC23×D149C22
cosocleC2×D149C24
LCSG ▷ C149
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

656 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#10597010, C4×(C2×#10597010)⋊C4, #34059866, …
maximal normal subgroup of#95×#10597010, C4×(C2×#10597010)⋊C4, #34059866, …
maximal quotient ofC2×C42×#10597010, C22×(C2×#10597010)⋊C4, C2×#23750561, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1609);