Finite Group Databasebeta

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C121×(C19⋊C3)⋊C4 #42119910

order27588
automorphism?
homologyAbelianization (H1) = C3×C4×C121 · Schur multiplier (H2) = C1

Aliases

direct productC121×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C121)
unambiguous semidirect productDic19⋊(C3×C121)
unambiguous semidirect product(Dic19×C121)⋊C3

Splittings

derived, SylowC19 ⋊ C3×C4×C121
HallDic19×C121 ⋊ C3
HallC19⋊C3×C121 ⋊ C4
HallC19×C121 ⋊ C3×C4
HallDic19 ⋊ C3×C121
HallC19⋊C3 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C121D19⋊C3
commutator, hypocenterC19C3×C4×C121
FrattiniC2×C11C11×D19⋊C3
FittingC2×C19×C121C2×C3
socle, cosocleC2×C11×C19C2×C3×C11
prime radicalC2×C11×C19⋊C3C2×C11
LCSG ▷ C19
UCSC1 ◁ C2×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9196

Conjugacy classes & character table

2178 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 2);