Finite Group Databasebeta

C2×#19104668 #23781698

order10432
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19104668

Splittings

SylowC163 ⋊ C2×#107

Subgroups

subgroupG/H
centerC23C22⋊D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
FittingC2×C4⋊C4×C163C2
socle, prime radicalC23×C163D4
cosocleC2×C4×C163C23
hypercenterC2×C4⋊C4D163
hypocenterC163C2×#107
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1648 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35214428, C4×#19104668, #35214432, …
maximal normal subgroup of#35214428, C4×#19104668, #35214432, …
maximal quotient ofC2×#23781417, #35213294, #35213310, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 582);