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C17×C3⋊(C11⋊Dic11) #37590591

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

Aliases

direct productC17×C3⋊(C11⋊Dic11)
unambiguous semidirect productC3⋊(C17×C11⋊Dic11)
unambiguous semidirect productC11⋊(C17×Dic33)

Splittings

derived, HallC3×C112 ⋊ C4×C17
HallC3×C112×C17 ⋊ C4
HallC112×C17 ⋊ Dic3
SylowC112 ⋊ Dic3×C17
HallC3×C17 ⋊ C11⋊Dic11
SylowC3 ⋊ C17×C11⋊Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C17C3⋊(C11⋊D11)
commutator, hypocenterC3×C112C4×C17
FrattiniC2C17×C3⋊(C11⋊D11)
Fitting, socle, prime radicalC2×C3×C112×C17C2
cosocleC2×C3×C112C2×C17
LCSG ▷ C3×C112
UCSC1 ◁ C2×C17

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24684

Conjugacy classes & character table

6222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24684, 37);