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C3×Dic157⋊C13 #37587564

order24492
automorphism?
homologyAbelianization (H1) = C3×C4×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic157⋊C13
unambiguous semidirect product(C3×Dic157)⋊C13

Splittings

derived, SylowC157 ⋊ C3×C4×C13
HallC3×C157⋊C13 ⋊ C4
HallC157⋊C13 ⋊ C3×C4
HallC3×Dic157 ⋊ C13
HallDic157 ⋊ C3×C13
HallC3×C157 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C3D157⋊C13
commutator, hypocenterC157C3×C4×C13
FrattiniC2C3×D157⋊C13
Fitting, socleC2×C3×C157C2×C13
prime radicalC2×C3×C157⋊C13C2
cosocleC2×C157C2×C3×C13
LCSG ▷ C157
UCSC1 ◁ C2×C3

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24492, 15);