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C5×C11×C13×Dic11 #44538147

order31460
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C13×Dic11

Splittings

derivedC11 ⋊ C4×C5×C11×C13
HallC5×C112×C13 ⋊ C4
HallC112×C13 ⋊ C4×C5
HallC5×C112 ⋊ C4×C13
SylowC112 ⋊ C4×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C13D11
commutator, hypocenterC11C4×C5×C11×C13
FrattiniC2C5×C11×C13×D11
Fitting, socle, prime radicalC2×C5×C112×C13C2
cosocleC2×C11C2×C5×C11×C13
LCSG ▷ C11
UCSC1 ◁ C2×C5×C11×C13

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2860

Conjugacy classes & character table

10010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31460, 87);