Finite Group Databasebeta

#108×D163 #23781709

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

Aliases

direct product#108×D163

Splittings

Fitting#108×C163 ⋊ C2
SylowC163 ⋊ C2×#108

Subgroups

subgroupG/H
centerC4D4×D163
commutatorC4×C163C22×C4
FrattiniC2×C4C22×D163
Fitting#108×C163C2
socleC2×C163C2×C4⋊C4
prime radicalC22×D163Q8
cosocleC2×C4×C163C23
hypercenter#108D163
hypocenterC163C2×#108
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C4 ◁ C2×C4 ◁ #108

106 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1162 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#359×D163, #35216262, #361×D163, …
maximal normal subgroup of#359×D163, #35216262, #361×D163, …
maximal quotient of#334×D163, #335×D163, #35213281, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 593);