Finite Group Databasebeta

← Prev (#24924653) Next (#24924655) →

C22×#14582089 #24924654

order10768
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14582089
unambiguous semidirect productD673⋊(C2×C4)

Splittings

Fitting, socleC22×C673 ⋊ C4
derived, SylowC673 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC22#14582089
commutator, hypocenterC673C22×C4
FrattiniC1G
Fitting, socleC22×C673C4
prime radicalC22×D673C2
cosocleD673C23
LCSG ▷ C673
UCSC1 ◁ C22

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

688 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14582089)⋊C4, C2×C4×#14582089, C2×C22⋊#14582089, …
maximal normal subgroup of(C2×#14582089)⋊C4, C2×C4×#14582089, C2×C22⋊#14582089, …
maximal quotient ofC2×C4×#14582089, C2×C22⋊#14582089, C2×C4⋊#14582089, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10768, 51);