Finite Group Databasebeta

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C107×(C19⋊C3)⋊C4 #37567327

order24396
automorphism?
homologyAbelianization (H1) = C3×C4×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C107)
unambiguous semidirect productDic19⋊(C3×C107)
unambiguous semidirect product(Dic19×C107)⋊C3

Splittings

derived, SylowC19 ⋊ C3×C4×C107
HallDic19×C107 ⋊ C3
HallC19⋊C3×C107 ⋊ C4
HallC19×C107 ⋊ C3×C4
HallDic19 ⋊ C3×C107
HallC19⋊C3 ⋊ C4×C107

Subgroups

subgroupG/H
center, hypercenterC2×C107D19⋊C3
commutator, hypocenterC19C3×C4×C107
FrattiniC2C107×D19⋊C3
Fitting, socleC2×C19×C107C2×C3
prime radicalC2×C19⋊C3×C107C2
cosocleC2×C19C2×C3×C107
LCSG ▷ C19
UCSC1 ◁ C2×C107

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8132

Conjugacy classes & character table

1926 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24396, 11);