Finite Group Databasebeta

← Prev (#26012499) Next (#26012501) →

C2×#19149748 #26012500

order11072
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19149748
unambiguous semidirect productD173⋊#107

Splittings

FittingC2×C8×C173 ⋊ C4
SylowC173 ⋊ C2×#107

Subgroups

subgroupG/H
centerC22C4⋊#10621924
commutatorC4×C173C22×C4
FrattiniC4C22×#10621924
FittingC2×C8×C173C4
socleC22×C173C4⋊C4
prime radicalC22×D173D4
cosocleC4×D173C23
hypercenterC2×C8#10621924
hypocenterC173C2×#107
LCSG ▷ C4×C173 ▷ C2×C173 ▷ C173
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

716 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#36368620, #36368621, #36368638, …
maximal normal subgroup of#36368620, #36368621, #36368638, …
maximal quotient ofC2×#26012354, D173⋊#335, C2×#26012355, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11072, 1558);