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M16×#10597010 #23750585

order9536
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×#10597010

Splittings

FittingM16×C149 ⋊ C4
SylowC149 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC4C22×#10597010
commutator, socleC2×C149C2×C42
FittingM16×C149C4
prime radicalC22×D149C2×C4
cosocleC4×D149C23
hypercenterM16#10597010
hypocenterC149C4×M16
LCSG ▷ C2×C149 ▷ C149
UCSC1 ◁ C4 ◁ M16

142 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

410 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#100×#10597010, #101×#10597010, #104×#10597010, …
maximal normal subgroup of#100×#10597010, #101×#10597010, #104×#10597010, …
maximal quotient ofM16×#11924753, #34059889, #34059892, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9536, 1509);