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C4×C23×#66526 #44499642

order30636
automorphism?
homologyAbelianization (H1) = C4×C9×C23 · Schur multiplier (H2) = C1

Aliases

direct productC4×C23×#66526

Splittings

Fitting, HallC4×C23×C37 ⋊ C9
derived, SylowC37 ⋊ C4×C9×C23
HallC23×C37 ⋊ C4×C9
HallC4×C37 ⋊ C9×C23

Subgroups

subgroupG/H
center, hypercenterC4×C23#66526
commutator, hypocenterC37C4×C9×C23
FrattiniC2C2×C23×#66526
FittingC4×C23×C37C9
socleC2×C23×C37C2×C9
prime radicalC2×C23×C37⋊C3C2×C3
cosocleC2×C37⋊C3C2×C3×C23
LCSG ▷ C37
UCSC1 ◁ C4×C23

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3404

Conjugacy classes & character table

1196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 45);