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C3×Dic15×C173 #44528153

order31140
automorphism?
homologyAbelianization (H1) = C3×C4×C173 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic15×C173
unambiguous semidirect productC3⋊(C3×Dic5×C173)

Splittings

derivedC3×C5 ⋊ C3×C4×C173
HallC32×C5×C173 ⋊ C4
HallC32×C173 ⋊ Dic5
HallC5×C173 ⋊ C3×Dic3
HallC32×C5 ⋊ C4×C173
SylowC32 ⋊ Dic5×C173
SylowC5 ⋊ C3×Dic3×C173

Subgroups

subgroupG/H
center, hypercenterC2×C3×C173D15
commutator, hypocenterC3×C5C3×C4×C173
FrattiniC2C3×D15×C173
Fitting, socle, prime radicalC2×C32×C5×C173C2
cosocleC2×C3×C5C2×C3×C173
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C173

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10380

Conjugacy classes & character table

9342 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31140, 43);