Finite Group Databasebeta

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C4×#14579126 #23765749

order10112
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14579126

Splittings

SylowC79 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D79
commutatorC2×C79C22×C42
FrattiniC23C23×D79
FittingC4×C4⋊C4×C79C2
socle, prime radical, cosocleC23×C79C24
hypercenterC4×C4⋊C4D79
hypocenterC79C42×Q8
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1640 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#34178865, #34178875, #34178885, …
maximal normal subgroup of#34178865, #34178875, #34178885, …
maximal quotient ofC4×#19098414, C4×C4⋊C4×Dic79, #34209441, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10112, 6859);