Finite Group Databasebeta

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C22×(C79⋊C9)⋊C13 #49149386

order36972
automorphism?
homologyAbelianization (H1) = C22×C9×C13 · Schur multiplier (H2) = C2

Aliases

direct productC22×(C79⋊C9)⋊C13
unambiguous semidirect product(C22×C79⋊C9)⋊C13

Splittings

derived, SylowC79 ⋊ C22×C9×C13
HallC22×C79⋊C13 ⋊ C9
HallC22×C79⋊C9 ⋊ C13
HallC79⋊C13 ⋊ C22×C9
HallC79⋊C9 ⋊ C22×C13
HallC22×C79 ⋊ C9×C13

Subgroups

subgroupG/H
center, hypercenterC22×C3(C79⋊C3)⋊C13
commutator, hypocenterC79C22×C9×C13
FrattiniC3C22×(C79⋊C3)⋊C13
Fitting, socleC22×C3×C79C3×C13
prime radicalC22×C3×C79⋊C13C3
cosocleC3×C79C22×C3×C13
LCSG ▷ C79
UCSC1 ◁ C22×C3

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2844

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36972, 34);