Finite Group Databasebeta

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C3×C11×C11⋊#1043 #49137735

order36300
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C11⋊#1043
unambiguous semidirect productC11⋊(C3×C11×#1043)

Splittings

Fitting, socle, HallC3×C52×C112 ⋊ C4
derivedC52×C11 ⋊ C3×C4×C11
HallC52×C112 ⋊ C3×C4
HallC3×C112 ⋊ #1043
SylowC112 ⋊ C3×#1043
HallC3×C52 ⋊ C11×Dic11
SylowC52 ⋊ C3×C11×Dic11

Subgroups

subgroupG/H
center, hypercenterC3×C11C11⋊#1043
commutator, hypocenterC52×C11C3×C4×C11
FrattiniC1G
Fitting, socleC3×C52×C112C4
prime radicalC3×C112×C5⋊D5C2
cosocleC11×C5⋊D5C2×C3×C11
LCSG ▷ C52×C11
UCSC1 ◁ C3×C11

352 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

2640 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36300, 871);