Finite Group Databasebeta

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C4×#17989464 #34008297

order18688
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#17989464

Splittings

FittingC4×C22⋊C4×C73 ⋊ C4
SylowC73 ⋊ C4×#342

Subgroups

subgroupG/H
centerC2×C4(C2×#64408)⋊C4
commutatorC22×C73C43
FrattiniC24C22×#64408
FittingC4×C22⋊C4×C73C4
socleC22×C73C2×#95
prime radical, cosocleC24×D73C23
hypercenterC4×C22⋊C4#64408
hypocenterC73C4×#342
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2336

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18688, 1091881);