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C19×Dic23⋊C11 #34063643

order19228
automorphism?
homologyAbelianization (H1) = C4×C11×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic23⋊C11
unambiguous semidirect productDic23⋊(C11×C19)
unambiguous semidirect product(C23⋊C11)⋊(C4×C19)
unambiguous semidirect product(C19×Dic23)⋊C11

Splittings

derived, SylowC23 ⋊ C4×C11×C19
HallC19×C23⋊C11 ⋊ C4
HallC19×Dic23 ⋊ C11
HallC19×C23 ⋊ C4×C11
HallC23⋊C11 ⋊ C4×C19
HallDic23 ⋊ C11×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19AGL(1,𝔽23)
commutator, hypocenterC23C4×C11×C19
FrattiniC2C19×AGL(1,𝔽23)
Fitting, socleC2×C19×C23C2×C11
prime radicalC2×C19×C23⋊C11C2
cosocleC2×C23C2×C11×C19
LCSG ▷ C23
UCSC1 ◁ C2×C19

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1748

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19228, 10);