Finite Group Databasebeta

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C32×C5×Dic155 #42124666

order27900
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic155

Splittings

derivedC5×C31 ⋊ C32×C4×C5
HallC32×C52×C31 ⋊ C4
HallC52×C31 ⋊ C32×C4
HallC32×C31 ⋊ C5×Dic5
HallC32×C52 ⋊ Dic31
SylowC31 ⋊ C32×C5×Dic5
SylowC52 ⋊ C32×Dic31

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D155
commutator, hypocenterC5×C31C32×C4×C5
FrattiniC2C32×C5×D155
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C5×C31C2×C32×C5
LCSG ▷ C5×C31
UCSC1 ◁ C2×C32×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7110 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 413);