Finite Group Databasebeta

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C2×Q8×#10597845 #23758338

order10048
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#10597845
unambiguous semidirect productD157⋊(C4×Q8)

Splittings

FittingC2×Q8×C157 ⋊ C4
SylowC157 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#10597845
commutatorC2×C157C23×C4
FrattiniC2C23×#10597845
FittingC2×Q8×C157C4
socleC22×C157C22×C4
prime radicalC22×D157C23
cosocleC2×D157C24
hypercenterC2×Q8#10597845
hypocenterC157C2×C4×Q8
LCSG ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#101×#10597845, #103×#10597845, #34115909, …
maximal normal subgroup of#101×#10597845, #103×#10597845, #34115909, …
maximal quotient ofC2×C4⋊C4×#10597845, C4×Q8×#10597845, C2×#23758222, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1614);