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C32×Dic53⋊C13 #37613634

order24804
automorphism?
homologyAbelianization (H1) = C32×C4×C13 · Schur multiplier (H2) = C3

Aliases

direct productC32×Dic53⋊C13
unambiguous semidirect productDic53⋊(C32×C13)
unambiguous semidirect product(C3×Dic53)⋊(C3×C13)
unambiguous semidirect product(C32×Dic53)⋊C13

Splittings

derived, SylowC53 ⋊ C32×C4×C13
HallC32×C53⋊C13 ⋊ C4
HallC32×Dic53 ⋊ C13
HallC53⋊C13 ⋊ C32×C4
HallC32×C53 ⋊ C4×C13
HallDic53 ⋊ C32×C13

Subgroups

subgroupG/H
center, hypercenterC2×C32D53⋊C13
commutator, hypocenterC53C32×C4×C13
FrattiniC2C32×D53⋊C13
Fitting, socleC2×C32×C53C2×C13
prime radicalC2×C32×C53⋊C13C2
cosocleC2×C53C2×C32×C13
LCSG ▷ C53
UCSC1 ◁ C2×C32

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1908

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24804, 66);