Finite Group Databasebeta

C2×#19104679 #23782089

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

Aliases

direct productC2×#19104679

Splittings

SylowC163 ⋊ C2×SD32

Subgroups

subgroupG/H
centerC22#14579684
commutator, cosocleC8×C163C23
FrattiniC8C22×D163
Fitting, prime radicalC2×D8×C163C2
socleC22×C163D8
hypercenterC2×D8D163
hypocenterC163C2×SD32
LCSG ▷ C8×C163 ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

90 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1156 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×#19104679, #35216391, #35216397, …
maximal normal subgroup ofC4×#19104679, #35216391, #35216397, …
maximal quotient ofC2×#23781466, C2×#23781468, C2×#23781492, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 973);