Finite Group Databasebeta

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C3×C11⋊#10625194 #37567584

order24420
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11⋊#10625194
unambiguous semidirect productC11⋊(C3×#10625194)

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C4
derived, HallC5×C11×C37 ⋊ C3×C4
HallC3×C11×C37 ⋊ Dic5
HallC3×C5×C37 ⋊ Dic11
HallC11×C37 ⋊ C3×Dic5
HallC5×C37 ⋊ C3×Dic11
HallC3×C5×C11 ⋊ #3866
HallC3×C37 ⋊ Dic55
HallC5×C11 ⋊ C3×#3866
SylowC37 ⋊ C3×Dic55
HallC3×C11 ⋊ #10625194
HallC3×C5 ⋊ C11⋊#3866
SylowC11 ⋊ C3×#10625194
SylowC5 ⋊ C3×C11⋊#3866

Subgroups

subgroupG/H
center, hypercenterC3C11⋊#10625194
commutator, hypocenterC5×C11×C37C3×C4
FrattiniC1G
Fitting, socleC3×C5×C11×C37C4
prime radicalC3×C5×C11×D37C2
cosocleC5×C11×D37C2×C3
LCSG ▷ C5×C11×C37
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

1659 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 105);