Finite Group Databasebeta

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C4×#17989218 #33245149

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

Aliases

direct productC4×#17989218

Splittings

SylowC73 ⋊ C4×#544

Subgroups

subgroupG/H
centerC22×C4C23×D73
commutatorC22×C73C24×C4
FrattiniC23C24×D73
FittingC2×C4×C4⋊C4×C73C2
socle, cosocleC23×C73C25
prime radicalC24×C73C24
hypercenterC2×C4×C4⋊C4D73
hypocenterC73C4×#544
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×C4×C4⋊C4

2210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9344

Conjugacy classes & character table

2968 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 328733);