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M16×D316 #23772138

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×D316

Splittings

FittingC4×M16×C79 ⋊ C2
SylowC79 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D79
commutator, socleC22×C79C23×C4
FittingC4×M16×C79C2
prime radicalC22×D316C4
cosocleC2×C4×C79C24
hypercenterC4×M16D79
hypocenterC79D4×M16
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×M16

544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1610 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34182596, #34182600, #34182610, …
maximal normal subgroup of#34182596, #34182600, #34182610, …
maximal quotient ofM16×D632, #34259701, M16×#11929613, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 13248);