Finite Group Databasebeta

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C22×#17989536 #34030542

order18688
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#17989536
unambiguous semidirect productD73⋊(C2×#387)

Splittings

FittingC22×C4⋊C4×C73 ⋊ C4
SylowC73 ⋊ C22×#387

Subgroups

subgroupG/H
centerC24C22×#64408
commutatorC22×C73C24×C4
FrattiniC22C24×#64408
FittingC22×C4⋊C4×C73C4
socleC24×C73C22×C4
prime radicalC24×D73C23
cosocleC22×D73C25
hypercenterC22×C4⋊C4#64408
hypocenterC73C22×#387
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C22×C4⋊C4

4286 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4672

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1114126);