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C2×#19104654 #23781645

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

Aliases

direct productC2×#19104654

Splittings

SylowC163 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic163
commutatorC22×C163C22×C4
FrattiniC2×C4C22×D163
FittingC22×Q8×C163C2
socleC22×C163C22⋊C4
prime radicalC23×C163C2×C4
cosocleC2×C4×C163C23
hypercenterC22×Q8D163
hypocenterC163C2×#101
LCSG ▷ C22×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1642 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#35212662, #35212663, C4×#19104654, …
maximal normal subgroup of#35212662, #35212663, C4×#19104654, …
maximal quotient ofC2×#23781391, #35212860, #35212866, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10432, 529);