Finite Group Databasebeta

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C3×Dic3×C23×C29 #37562175

order24012
automorphism?
homologyAbelianization (H1) = C3×C4×C23×C29 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C23×C29
unambiguous semidirect productC3⋊(C3×C4×C23×C29)

Splittings

derivedC3 ⋊ C3×C4×C23×C29
HallC32×C23×C29 ⋊ C4
HallC32×C29 ⋊ C4×C23
HallC32×C23 ⋊ C4×C29
SylowC32 ⋊ C4×C23×C29

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23×C29D3
commutator, hypocenterC3C3×C4×C23×C29
FrattiniC2C3×D3×C23×C29
Fitting, socle, prime radicalC2×C32×C23×C29C2
cosocleC2×C3C2×C3×C23×C29
LCSG ▷ C3
UCSC1 ◁ C2×C3×C23×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8004

Conjugacy classes & character table

12006 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24012, 37);