Finite Group Databasebeta

C2×#19104671 #23781711

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

Aliases

direct productC2×#19104671

Splittings

SylowC163 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D652
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
FittingC22×C8×C163C2
socleC22×C163C4⋊C4
prime radicalC23×C163Q8
cosocleC2×C4×C163C23
hypercenterC22×C8D163
hypocenterC163C2×#108
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2620 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35212629, #35212630, #35212631, …
maximal normal subgroup of#35212629, #35212630, #35212631, …
maximal quotient ofC2×#23781416, C2×#23781418, #35213284, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 595);