Finite Group Databasebeta

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C32×C11×C13×Dic5 #38787994

order25740
automorphism?
homologyAbelianization (H1) = C32×C4×C11×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×C11×C13×Dic5

Splittings

derived, SylowC5 ⋊ C32×C4×C11×C13
HallC32×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ C32×C4
HallC32×C5×C13 ⋊ C4×C11
HallC32×C5×C11 ⋊ C4×C13
HallC5×C13 ⋊ C32×C4×C11
HallC5×C11 ⋊ C32×C4×C13
HallC32×C5 ⋊ C4×C11×C13

Subgroups

subgroupG/H
center, hypercenterC2×C32×C11×C13D5
commutator, hypocenterC5C32×C4×C11×C13
FrattiniC2C32×D5×C11×C13
Fitting, socle, prime radicalC2×C32×C5×C11×C13C2
cosocleC2×C5C2×C32×C11×C13
LCSG ▷ C5
UCSC1 ◁ C2×C32×C11×C13

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25740

Conjugacy classes & character table

10296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 225);