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C11×C37×Dic15 #37567495

order24420
automorphism?
homologyAbelianization (H1) = C4×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC11×C37×Dic15
unambiguous semidirect productC3⋊(C11×Dic5×C37)

Splittings

derived, HallC3×C5 ⋊ C4×C11×C37
HallC3×C5×C11×C37 ⋊ C4
HallC5×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ Dic5
HallC3×C5×C37 ⋊ C4×C11
HallC5×C37 ⋊ C11×Dic3
HallC3×C5×C11 ⋊ C4×C37
HallC3×C37 ⋊ C11×Dic5
HallC5×C11 ⋊ Dic3×C37
HallC3×C11 ⋊ Dic5×C37
SylowC5 ⋊ C11×Dic3×C37
SylowC3 ⋊ C11×Dic5×C37

Subgroups

subgroupG/H
center, hypercenterC2×C11×C37D15
commutator, hypocenterC3×C5C4×C11×C37
FrattiniC2C11×D15×C37
Fitting, socle, prime radicalC2×C3×C5×C11×C37C2
cosocleC2×C3×C5C2×C11×C37
LCSG ▷ C3×C5
UCSC1 ◁ C2×C11×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24420

Conjugacy classes & character table

7326 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 16);