Finite Group Databasebeta

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C4×#14579142 #23765918

order10112
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14579142

Splittings

SylowC79 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC2×C4×D4×C79C2
socle, cosocleC23×C79C24
prime radicalC22×D4×C79C22
hypercenterC2×C4×D4D79
hypocenterC79C4×#123
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

688 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#34182957, #34182959, #34182967, …
maximal normal subgroup of#34182957, #34182959, #34182967, …
maximal quotient ofC4×#19098443, C4×#19098451, C4×#19098435, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7028);