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C32×C5×Dic145 #39908018

order26100
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic145

Splittings

derivedC5×C29 ⋊ C32×C4×C5
HallC32×C52×C29 ⋊ C4
HallC52×C29 ⋊ C32×C4
HallC32×C29 ⋊ C5×Dic5
HallC32×C52 ⋊ Dic29
SylowC29 ⋊ C32×C5×Dic5
SylowC52 ⋊ C32×Dic29

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D145
commutator, hypocenterC5×C29C32×C4×C5
FrattiniC2C32×C5×D145
Fitting, socle, prime radicalC2×C32×C52×C29C2
cosocleC2×C5×C29C2×C32×C5
LCSG ▷ C5×C29
UCSC1 ◁ C2×C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5220

Conjugacy classes & character table

6660 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 252);