Finite Group Databasebeta

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C2×#19098621 #23772023

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#19098621

Splittings

SylowC79 ⋊ C2×#433

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC2×C4C23×D79
FittingC2×C22⋊C8×C79C2
socleC23×C79C22×C4
prime radicalC24×C79C2×C4
cosocleC2×C4×C79C24
hypercenterC2×C22⋊C8D79
hypocenterC79C2×#433
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

412 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1616 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34197472, C4×#19098621, #34286417, …
maximal normal subgroup of#34197472, C4×#19098621, #34286417, …
maximal quotient ofC2×#23763150, C2×#23763168, C2×#23763256, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 13133);