Finite Group Databasebeta

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Cayley diagram

D4×D25 #87745

order400
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C23

Aliases

direct productD4×D25

Splittings

FittingD4×C25 ⋊ C2
SylowC25 ⋊ C2×D4

Subgroups

subgroupG/H
centerC2C22×D25
commutator, cosocleC2×C25C23
Frattini, socleC2×C5C22×D5
FittingD4×C25C2
hypercenterD4D25
hypocenterC25C2×D4
LCSG ▷ C2×C25 ▷ C25
UCSC1 ◁ C2 ◁ D4

81 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 100

A minimal faithful permutation representation — 3 generators on 29 points:

(2,4)(3,7)(5,10)(6,13)(8,16)(9,15)(11,18)(12,20)(14,22)(17,23)(19,24)(21,25);(1,14,18,19,13,3,23,5,25,4,8,15,12,20,9,16,2,21,10,17,7,6,24,11,22)(27,29);(26,27)(28,29)

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11716424, D8×D25, #11716473, …
maximal normal subgroup of#11716424, D8×D25, #11716473, …
maximal quotient of#11716440, C22⋊C4×D25, #11716443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(400, 39);