Finite Group Databasebeta

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C3×C23×Dic115 #44540705

order31740
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic115
unambiguous semidirect productC23⋊(C3×Dic5×C23)

Splittings

derivedC5×C23 ⋊ C3×C4×C23
HallC3×C5×C232 ⋊ C4
HallC5×C232 ⋊ C3×C4
HallC3×C232 ⋊ Dic5
SylowC232 ⋊ C3×Dic5
HallC3×C5 ⋊ C23×Dic23
SylowC5 ⋊ C3×C23×Dic23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D115
commutator, hypocenterC5×C23C3×C4×C23
FrattiniC2C3×C23×D115
Fitting, socle, prime radicalC2×C3×C5×C232C2
cosocleC2×C5×C23C2×C3×C23
LCSG ▷ C5×C23
UCSC1 ◁ C2×C3×C23

136 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1380

Conjugacy classes & character table

8142 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31740, 43);