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C167×(C19⋊C3)⋊C4 #49185153

order38076
automorphism?
homologyAbelianization (H1) = C3×C4×C167 · Schur multiplier (H2) = C1

Aliases

direct productC167×(C19⋊C3)⋊C4
unambiguous semidirect product(C19⋊C3)⋊(C4×C167)
unambiguous semidirect productDic19⋊(C3×C167)
unambiguous semidirect product(Dic19×C167)⋊C3

Splittings

derived, SylowC19 ⋊ C3×C4×C167
HallDic19×C167 ⋊ C3
HallC19⋊C3×C167 ⋊ C4
HallC19×C167 ⋊ C3×C4
HallDic19 ⋊ C3×C167
HallC19⋊C3 ⋊ C4×C167

Subgroups

subgroupG/H
center, hypercenterC2×C167D19⋊C3
commutator, hypocenterC19C3×C4×C167
FrattiniC2D19⋊C3×C167
Fitting, socleC2×C19×C167C2×C3
prime radicalC2×C19⋊C3×C167C2
cosocleC2×C19C2×C3×C167
LCSG ▷ C19
UCSC1 ◁ C2×C167

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12692

Conjugacy classes & character table

3006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38076, 11);