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C4×C9×C79⋊C13 #49149354

order36972
automorphism?
homologyAbelianization (H1) = C4×C9×C13 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C79⋊C13
unambiguous semidirect product(C4×C9×C79)⋊C13

Splittings

Fitting, HallC4×C9×C79 ⋊ C13
derived, SylowC79 ⋊ C4×C9×C13
HallC9×C79 ⋊ C4×C13
HallC4×C79 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC4×C9C79⋊C13
commutator, hypocenterC79C4×C9×C13
FrattiniC2×C3C2×C3×C79⋊C13
FittingC4×C9×C79C13
socle, cosocleC2×C3×C79C2×C3×C13
prime radicalC2×C3×C79⋊C13C2×C3
LCSG ▷ C79
UCSC1 ◁ C4×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2844

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 2);