Finite Group Databasebeta

← Prev (#23758226) Next (#23758228) →

C2×C8×#10597845 #23758227

order10048
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C8×#10597845

Splittings

FittingC2×C8×C157 ⋊ C4
derived, SylowC157 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C8#10597845
commutator, hypocenterC157C2×C4×C8
FrattiniC4C22×#10597845
FittingC2×C8×C157C4
socleC22×C157C42
prime radicalC22×D157C2×C4
cosocleC4×D157C23
LCSG ▷ C157
UCSC1 ◁ C2×C8

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#10597845)⋊C16, #34115179, C4×C8×#10597845, …
maximal normal subgroup of(C2×#10597845)⋊C16, #34115179, C4×C8×#10597845, …
maximal quotient ofC2×C8×#11929441, C8×D157⋊C8, C2×#11929441⋊C8, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10048, 1503);