Finite Group Databasebeta

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C22⋊C4×#11924007 #33007402

order18688
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC22⋊C4×#11924007

Splittings

SylowC73 ⋊ C22⋊C4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC24C23×D73
commutatorC22×C73C22×C42
FittingC2×C4×C22⋊C4×C73C2
socle, cosocleC24×C73C24
prime radicalC25×C73C23
hypercenterC2×C4×C22⋊C4D73
hypocenterC73C22⋊C4×C4⋊C4
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

2574 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 90986);