Finite Group Databasebeta

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C32×C5×Dic5×C31 #42124667

order27900
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C32×C4×C5×C31 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×Dic5×C31

Splittings

derivedC5 ⋊ C32×C4×C5×C31
HallC32×C52×C31 ⋊ C4
HallC52×C31 ⋊ C32×C4
HallC32×C52 ⋊ C4×C31
SylowC52 ⋊ C32×C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5×C31D5
commutator, hypocenterC5C32×C4×C5×C31
FrattiniC2C32×C5×D5×C31
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C5C2×C32×C5×C31
LCSG ▷ C5
UCSC1 ◁ C2×C32×C5×C31

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 414);