Finite Group Databasebeta

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C4⋊C4×#11924038 #34020221

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4⋊C4×#11924038

Splittings

SylowC73 ⋊ C4⋊C4×M16

Subgroups

subgroupG/H
center, FrattiniC23C23×#64408
commutatorC22×C73C22×C42
FittingC4×C4⋊C4×C73C4
socleC23×C73C23×C4
prime radicalC23×D73C22×C4
cosocleC22×Dic73C24
hypercenterC4×C4⋊C4#64408
hypocenterC73C4⋊C4×M16
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C4×C4⋊C4

1242 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1103805);