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C4×C23×C29⋊C7 #32916355

order18676
automorphism?
homologyAbelianization (H1) = C4×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C23×C29⋊C7
unambiguous semidirect product(C4×C29)⋊(C7×C23)
unambiguous semidirect product(C4×C23×C29)⋊C7

Splittings

Fitting, HallC4×C23×C29 ⋊ C7
derived, SylowC29 ⋊ C4×C7×C23
HallC23×C29 ⋊ C4×C7
HallC4×C29 ⋊ C7×C23

Subgroups

subgroupG/H
center, hypercenterC4×C23C29⋊C7
commutator, hypocenterC29C4×C7×C23
FrattiniC2C2×C23×C29⋊C7
FittingC4×C23×C29C7
socleC2×C23×C29C2×C7
prime radicalC2×C23×C29⋊C7C2
cosocleC2×C29C2×C7×C23
LCSG ▷ C29
UCSC1 ◁ C4×C23

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2668

Conjugacy classes & character table

1012 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18676, 2);