Finite Group Databasebeta

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M16×D332 #24916201

order10624
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×D332

Splittings

FittingC4×M16×C83 ⋊ C2
SylowC83 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D83
commutator, socleC22×C83C23×C4
FittingC4×M16×C83C2
prime radicalC22×D332C4
cosocleC2×C4×C83C24
hypercenterC4×M16D83
hypocenterC83D4×M16
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×M16

544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1690 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35298731, #35298735, #35298745, …
maximal normal subgroup of#35298731, #35298735, #35298745, …
maximal quotient ofM16×D664, #35375836, M16×#13050579, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10624, 13248);