Finite Group Databasebeta

← Prev (#37587566) Next (#37587568) →

C13×Dic157⋊C3 #37587567

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

Aliases

direct productC13×Dic157⋊C3

Splittings

derived, SylowC157 ⋊ C3×C4×C13
HallC13×Dic157 ⋊ C3
HallC13×C157⋊C3 ⋊ C4
HallC13×C157 ⋊ C3×C4
HallDic157 ⋊ C3×C13
HallC157⋊C3 ⋊ C4×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13D157⋊C3
commutator, hypocenterC157C3×C4×C13
FrattiniC2C13×D157⋊C3
Fitting, socleC2×C13×C157C2×C3
prime radicalC2×C13×C157⋊C3C2
cosocleC2×C157C2×C3×C13
LCSG ▷ C157
UCSC1 ◁ C2×C13

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24492, 18);