Finite Group Databasebeta

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C3×C11×C17×Dic11 #37590599

order24684
automorphism?
homologyAbelianization (H1) = C3×C4×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×C17×Dic11
unambiguous semidirect productC11⋊(C3×C4×C11×C17)

Splittings

derivedC11 ⋊ C3×C4×C11×C17
HallC3×C112×C17 ⋊ C4
HallC112×C17 ⋊ C3×C4
HallC3×C112 ⋊ C4×C17
SylowC112 ⋊ C3×C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11×C17D11
commutator, hypocenterC11C3×C4×C11×C17
FrattiniC2C3×C11×C17×D11
Fitting, socle, prime radicalC2×C3×C112×C17C2
cosocleC2×C11C2×C3×C11×C17
LCSG ▷ C11
UCSC1 ◁ C2×C3×C11×C17

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2244

Conjugacy classes & character table

7854 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 45);