Finite Group Databasebeta

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M16×#10597845 #23758233

order10048
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productM16×#10597845

Splittings

FittingM16×C157 ⋊ C4
SylowC157 ⋊ C4×M16

Subgroups

subgroupG/H
center, FrattiniC4C22×#10597845
commutator, socleC2×C157C2×C42
FittingM16×C157C4
prime radicalC22×D157C2×C4
cosocleC4×D157C23
hypercenterM16#10597845
hypocenterC157C4×M16
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C4 ◁ M16

142 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#100×#10597845, #101×#10597845, #104×#10597845, …
maximal normal subgroup of#100×#10597845, #101×#10597845, #104×#10597845, …
maximal quotient ofM16×#11929441, #34115334, #34115337, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1509);