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C4×#16811482 #28301882

order13568
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16811482

Splittings

SylowC53 ⋊ C4×#332

Subgroups

subgroupG/H
centerC22×C4C22⋊#6157
commutatorC2×C4×C53C2×C42
FrattiniC22×C4C22×#6157
FittingC4×C4⋊C4×C53C4
socle, prime radicalC23×C53C2×C22⋊C4
cosocleC2×C4×Dic53C23
hypercenterC4×C4⋊C4#6157
hypocenterC53C4×#332
LCSG ▷ C2×C4×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×C4⋊C4

540 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13568

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1087358);