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C72×D195 #34062189

order19110
automorphism?
homologyAbelianization (H1) = C2×C72 · Schur multiplier (H2) = C7

Aliases

direct productC72×D195
unambiguous semidirect productC3⋊(C72×D65)
unambiguous semidirect productC5⋊(C72×D39)
unambiguous semidirect productC13⋊(C72×D15)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C2
derived, HallC3×C5×C13 ⋊ C2×C72
HallC5×C72×C13 ⋊ D3
HallC3×C72×C13 ⋊ D5
HallC3×C5×C72 ⋊ D13
HallC72×C13 ⋊ D15
HallC5×C72 ⋊ D39
HallC3×C72 ⋊ D65
HallC5×C13 ⋊ D3×C72
HallC3×C13 ⋊ C72×D5
HallC3×C5 ⋊ C72×D13
SylowC13 ⋊ C72×D15
SylowC5 ⋊ C72×D39
SylowC3 ⋊ C72×D65

Subgroups

subgroupG/H
center, hypercenterC72D195
commutator, cosocle, hypocenterC3×C5×C13C2×C72
FrattiniC1G
Fitting, socleC3×C5×C72×C13C2
LCSG ▷ C3×C5×C13
UCSC1 ◁ C72

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

4851 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC72×D13×D15, C7×D7×D195, C7×D91⋊D15, …
maximal normal subgroup ofC72×D13×D15, C7×D7×D195, C7×D91⋊D15, …
maximal quotient ofC72×Dic195, C2×C72×D195

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 182);