Finite Group Databasebeta

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C4×#14579160 #23765970

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

Aliases

direct productC4×#14579160

Splittings

SylowC79 ⋊ C4×C4⋊Q8

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC22×C79C23×C4
FrattiniC23C23×D79
FittingC4×C4⋊C4×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC4×C4⋊C4D79
hypocenterC79C4×C4⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

588 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#34188248, #34188252, #34188266, …
maximal normal subgroup of#34188248, #34188252, #34188266, …
maximal quotient ofC4×#19098462, C4×#19098460, C4×#19098459, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 7080);