Finite Group Databasebeta

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C4×#17984048 #31783133

order17536
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#17984048

Splittings

FittingC4×C22⋊C4×C137 ⋊ C2
SylowC137 ⋊ C42×D4

Subgroups

subgroupG/H
centerC22×C4C22×D137
commutatorC2×C137C22×C42
FrattiniC23C23×D137
FittingC4×C22⋊C4×C137C2
socle, cosocleC23×C137C24
prime radicalC22×C22⋊D137C22
hypercenterC4×C22⋊C4D137
hypocenterC137C42×D4
LCSG ▷ C2×C137 ▷ C137
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8768

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17536, 6854);