Finite Group Databasebeta

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C22⋊C4×C22⋊D137 #31783608

order17536
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22⋊C4×C22⋊D137

Splittings

FittingC22×C22⋊C4×C137 ⋊ C2
SylowC137 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D137
commutatorC22×C137C23×C4
FittingC22×C22⋊C4×C137C2
socle, cosocleC23×C137C24
prime radicalC23×C22⋊D137C2
hypercenterC22×C22⋊C4D137
hypocenterC137D4×C22⋊C4
LCSG ▷ C22×C137 ▷ C137
UCSC1 ◁ C23 ◁ C22×C22⋊C4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4384

Conjugacy classes & character table

2770 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 7329);