Finite Group Databasebeta

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C3×C23×Dic123 #46800409

order33948
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC3×C23×Dic123
unambiguous semidirect productC3⋊(C3×C23×Dic41)

Splittings

derivedC3×C41 ⋊ C3×C4×C23
HallC32×C23×C41 ⋊ C4
HallC23×C41 ⋊ C3×Dic3
HallC32×C41 ⋊ C4×C23
HallC32×C23 ⋊ Dic41
SylowC41 ⋊ C3×Dic3×C23
SylowC32 ⋊ C23×Dic41

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D123
commutator, hypocenterC3×C41C3×C4×C23
FrattiniC2C3×C23×D123
Fitting, socle, prime radicalC2×C32×C23×C41C2
cosocleC2×C3×C41C2×C3×C23
LCSG ▷ C3×C41
UCSC1 ◁ C2×C3×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11316

Conjugacy classes & character table

8694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33948, 36);