Finite Group Databasebeta

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C4×C4⋊C4×#6157 #28312683

order13568
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C23×C43

Aliases

direct productC4×C4⋊C4×#6157

Splittings

FittingC4×C4⋊C4×C53 ⋊ C4
SylowC53 ⋊ C42×C4⋊C4

Subgroups

subgroupG/H
centerC22×C4C22×#6157
commutatorC2×C53C2×C43
FrattiniC23C23×#6157
FittingC4×C4⋊C4×C53C4
socleC23×C53C23×C4
prime radical, cosocleC23×D53C24
hypercenterC4×C4⋊C4#6157
hypocenterC53C42×C4⋊C4
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

2478 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1098159);