Finite Group Databasebeta

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C112×(C19⋊C3)⋊C4 #42119944

order27588
automorphism?
homologyAbelianization (H1) = C3×C4×C112 · Schur multiplier (H2) = C11

Aliases

direct productC112×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C112)
unambiguous semidirect productDic19⋊(C3×C112)
unambiguous semidirect product(C11×Dic19)⋊(C3×C11)

Splittings

derived, SylowC19 ⋊ C3×C4×C112
HallC112×Dic19 ⋊ C3
HallC112×C19⋊C3 ⋊ C4
HallC112×C19 ⋊ C3×C4
HallDic19 ⋊ C3×C112
HallC19⋊C3 ⋊ C4×C112

Subgroups

subgroupG/H
center, hypercenterC2×C112D19⋊C3
commutator, hypocenterC19C3×C4×C112
FrattiniC2C112×D19⋊C3
Fitting, socleC2×C112×C19C2×C3
prime radicalC2×C112×C19⋊C3C2
cosocleC2×C19C2×C3×C112
LCSG ▷ C19
UCSC1 ◁ C2×C112

168 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, 36);